Flexible distributions for triple-goal estimates in two-stage hierarchical models

Computational Statistics and Data Analysis

Volumn 50, Issue 11, 2006, Pages 3243-3262

  Paddock, Susan M ^a   Ridgeway, Greg ^a   Lin, Rongheng ^b   Louis, Thomas A ^b  

^a RAND CORPORATION   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Bayesian statistics; League tables; Nonparametrics; Percentiles; Ranking; Robustness

Indexed keywords

MATHEMATICAL MODELS; NEURAL NETWORKS; OPTIMAL CONTROL SYSTEMS; PARAMETER ESTIMATION; ROBUSTNESS (CONTROL SYSTEMS); SPECIFICATIONS;

BAYESIAN STATISTICS; LEAGUE TABLES; NONPARAMETRICS; PERCENTILES; RANKING;

HIERARCHICAL SYSTEMS;

EID: 33646546385     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2005.05.008     Document Type: Article

References (33)

1. Antoniak C.E. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2 (1974) 1152-1174
2. Bryk A.S., and Raudenbush S.W. Hierarchical Linear Models (1992), Sage Publications, Inc., Newbury Park, CA
3. Christiansen C.L., and Morris C.N. Hierarchical Poisson regression modeling. J. Amer. Statist. Assoc. 92 (1997) 618-632
4. Congdon P. Bayesian Statistical Modeling (2001), Wiley, Chichester
5. Conlon, E.M., Louis, T.A., 1999. Addressing multiple goals in evaluating region-specific risk using Bayesian methods. In: Disease Mapping and Risk Assessment for Public Health, Wiley, Chichester, pp. 31-47.
6. Devine O.J., and Louis T.A. A constrained empirical Bayes estimator for incidence rates in areas with small populations. Statist. Med. 13 (1994) 1119-1133
7. Devine O.J., Louis T.A., and Halloran M.E. Empirical Bayes methods for stabilizing incidence rates before mapping. Epidemiology 5 (1994) 622-630
8. Escobar M.D. Estimating normal means with a Dirichlet process prior. J. Amer. Statist. Assoc. 89 (1994) 268-277
9. Escobar M.D., and West M. Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 (1995) 577-588
10. Gelman, A., 2005. Prior distributions for variance parameters in hierarchical models. Bayesian Anal., to appear.
11. Gelman A., and Price P.N. All maps of parameter estimates are misleading. Statist. Med. 18 (1999) 3221-3234
12. Ghosh M. Constrained Bayes estimation with applications. J. Amer. Statist. Assoc. 87 (1992) 533-540
13. Goldstein H., and Spiegelhalter D.J. League tables and their limitations: statistical issues in comparisons of institutional performance. J. Roy. Statist. Soc. Ser. A 159 (1996) 385-409
14. Laird N. Nonparametric maximum likelihood estimation of a mixing distribution. J. Amer. Statist. Assoc. 73 (1978) 805-811
15. Laird N.M., and Louis T.A. Empirical Bayes ranking methods. J. Ed. Statist. 14 (1989) 29-46
16. Laird N.M., and Louis T.A. Smoothing the non-parametric estimate of a prior distribution by roughening. A computational study. Computat. Statist. Data Anal. 12 (1991) 27-37
17. Landrum M.B., Bronskill S.E., and Normand S.-L.T. Analytic methods for constructing cross-sectional profiles of health care providers. Health Services Outcomes Res. Methodol. 1 1 (2000) 23-47
18. Lindley D.V., and Smith A.F.M. Bayes estimates for the linear model. J. Roy. Statist. Soc. Ser. B 34 (1972) 1-41
19. Liu J., Louis T.A., Pan W., Ma J., and Collins A. Methods for estimating and interpreting provider-specific, standardized mortality ratios. Health Services Outcomes Res. Methodol. 4 (2003) 135-149
20. Lockwood J.R., Louis T.A., and McCaffrey D.F. Uncertainty in rank estimation: implications for value-added modeling accountability systems. J. Ed. Behav. Statist. 27 3 (2002) 255-270
21. Louis T.A. Estimating a population of parameter values using Bayes and empirical Bayes methods. J. Amer. Statist. Assoc. 79 (1984) 393-398
22. MacEachern S., and Müller P. Estimating mixture of Dirichlet process models. J. Computat. Graphical Statist. 7 (1998) 223-238
23. McClellan, M., Staiger, D., 1999. The quality of health care providers. Technical Report 7327, National Bureau of Economic Research Working Paper.
24. Morris C.N. Parametric empirical Bayes inference: theory and applications. J. Amer. Statist. Assoc. 78 (1983) 47-65
25. Müller P., Erkanli A., and West M. Bayesian curve fitting using multivariate normal mixtures. Biometrika 83 (1996) 67-79
26. Ridgeway, G., Paddock, S.M., 2004. The HHSIM package, Version 0.3. Available at http://www.i-pensieri.com/gregr/hhsim.shtml.
27. Shen W., and Louis T.A. Triple-goal estimates in two-stage hierarchical models. J. Roy. Statist. Soc. Ser. B 60 (1998) 455-471
28. Shen W., and Louis T.A. Empirical Bayes estimation via the smoothing by roughening approach. J. Computat. Graphical Statist. 8 (1999) 800-823
29. Shen W., and Louis T.A. Triple-goal estimates for disease mapping. Statist. Med. 19 (2000) 2295-2308
30. Spiegelhalter, D., Thomas, A., Best, N., Lunn, D., 2004. WinBUGS with DoodleBUGS Version 1.4.1. Imperial College and Medical Research Council, UK.
31. Verdinelli I., and Wasserman L. Bayesian analysis of outlier problems using the Gibbs sampler. Statist. Comput. 1 (1991) 105-117
32. Wakefield J. Discussion of 'Some algebra and geometry for hierarchical models, applied to diagnostics'. J. Roy. Statist. Soc. Ser. B 60 (1998) 523-526
33. West M., Müller P., and Escobar M.D. Hierarchical priors and mixture models, with application in regression and density estimation. In: Freeman P.R., and Smith A.F.M. (Eds). Aspects of Uncertainty. A Tribute to D.V. Lindley (1994), Wiley, New York 363-386